There seems to be a lot of confusion about this and SE hasn't been entirely clear on it.

Here's what I'm pretty sure is happening:

The Warring Triad plotline is a side story, like Ravana EX and Bismarck EX, since it's the continuation of the story for those two battles.

However, there will be a certain point in the main story that is gated behind completing this plotline, so that the main story can reference its events.

This is the same as the Hard modes of Ifrit, Titan and Garuda being mandatory to pass a certain point of the ARR storyline.

They mentioned being able to choose whether to focus on the main story or the Warring Triad in the live letter, which is why I think this is the case. The confusion mainly stems from the fact that there's also EX versions of the Warring Triad, which is NOT story-related, and the term "main story" has been used to refer to the Normal version as opposed to the EX version.